The story revolves around a girl kidnapped from home and sold to a brothel, where she learns to sing, write, dance and captivate wealthy men. She later falls in love with a Muslim prince, but he refuses to marry her.
"Though Umrao Jaan is a story based in the 19th century, this story could take place anywhere in India today. This could be the story of so many girls," the former Miss World told reporters last week.
"This is a big phase for Aishwarya. She is the international face of Bollywood," a films trade analyst Pramod Natha told.
A local press report said the films represented a critical phase in Rai's Bollywood career, after just three of 30 movies she made in the past decade were hits at the box office.
"At 33, this is her last chance to prove herself in these movies," the Hindustan Times daily newspaper said last week, quoting trade analyst Amod Mehra.
The star's two other releases, a sequel to the hit biking gangster movie "Dhoom2," and "Guru," a film about the life of a business tycoon in India, are scheduled for release in the next two weeks.
Rai, a Cannes film festival favourite in recent years, was voted among the top 100 most influential people in the world by Time Magazine in 2004-05.